TY - JOUR
T1 - Tree indiscernibilities, revisited
AU - Kim, Byunghan
AU - Kim, Hyeung Joon
AU - Scow, Lynn
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2014/2
Y1 - 2014/2
N2 - We give definitions that distinguish between two notions of indiscernibility for a set {aη {divides} η ∈ ω>ω} that saw original use in Shelah [Classification theory and the number of non-isomorphic models (revised edition). North-Holland, Amsterdam, 1990], which we name s- and str-indiscernibility. Using these definitions and detailed proofs, we prove s- and str-modeling theorems and give applications of these theorems. In particular, we verify a step in the argument that TP is equivalent to TP1 or TP2 that has not seen explication in the literature. In the Appendix, we exposit the proofs of Shelah [Classification theory and the number of non-isomorphic models (revised edition). North-Holland, Amsterdam, 1990, App. 2.6, 2.7], expanding on the details.
AB - We give definitions that distinguish between two notions of indiscernibility for a set {aη {divides} η ∈ ω>ω} that saw original use in Shelah [Classification theory and the number of non-isomorphic models (revised edition). North-Holland, Amsterdam, 1990], which we name s- and str-indiscernibility. Using these definitions and detailed proofs, we prove s- and str-modeling theorems and give applications of these theorems. In particular, we verify a step in the argument that TP is equivalent to TP1 or TP2 that has not seen explication in the literature. In the Appendix, we exposit the proofs of Shelah [Classification theory and the number of non-isomorphic models (revised edition). North-Holland, Amsterdam, 1990, App. 2.6, 2.7], expanding on the details.
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U2 - 10.1007/s00153-013-0363-6
DO - 10.1007/s00153-013-0363-6
M3 - Article
AN - SCOPUS:84892495078
VL - 53
SP - 211
EP - 232
JO - Archive for Mathematical Logic
JF - Archive for Mathematical Logic
SN - 0933-5846
IS - 1-2
ER -